Photoluminescence of a low-density two-dimensional hole gas in a GaAs quantum well: Observation of valence-band Landau levels

We study the low-energy tail of the photoluminescence spectrum of a low-density two-dimensional hole gas in a magnetic field in a GaAs quantum well. A rich spectrum of lines is observed, and we show that it can be classified into two groups: the shake-up lines of the positively charged exciton ${(X}^{+}),$ and the recombination lines of a free hole with an electron bound to a donor ${(D}^{0}h).\mathrm{}$ An analysis of these transitions reveals a simple picture of equidistant hole Landau levels, with a cyclotron mass of ${0.6m}_0.$